Is sec^2(x)-tan^2(x)=sec(x)cos(x) ?

The answer to whether sec^2(x)-tan^2(x)=sec(x)cos(x) is True

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prove sec^2(x)-tan^2(x)=sec(x)cos(x)

prove

sec^{2} (x) - tan^{2} (x) = sec (x) cos (x)

True

Solution steps

sec^{2} (x) - tan^{2} (x) = sec (x) cos (x)

Manipulating right side

sec (x) cos (x)

Express with sin, cos

cos (x) sec (x)

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

= cos (x) \frac{1}{cos ( x )}

cos (x) \frac{1}{cos ( x )} = 1

cos (x) \frac{1}{cos ( x )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot cos ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= 1

= 1

= 1

Rewrite using trig identities

1

Use the Pythagorean identity:

tan^{2} (x) + 1 = sec^{2} (x)

1 = sec^{2} (x) - tan^{2} (x)

= sec^{2} (x) - tan^{2} (x)

= sec^{2} (x) - tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (4 x) = \frac{1}{2} + \frac{1}{2} cos (16 x)

\frac{( sec ^{2} ( t ) )}{sec ^{2} ( t ) - 1} = csc^{2} (t)

sin^{2} (x) = cos (2 x) + 2

1 + cos^{2} (x) = 2 - sin^{2} (x)

sin (\frac{3 π}{2} + 0) = - cos (0)

Is sec^2(x)-tan^2(x)=sec(x)cos(x) ?
The answer to whether sec^2(x)-tan^2(x)=sec(x)cos(x) is True